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The superconducting critical current density,  J  c , in hole doped cuprates show strong dependence on the doped hole content,  p , within the copper oxide plane(s). The doping dependent  J  c  mainly exhibits the variation of the intrinsic depairing critical current density as  p  is varied.  J  c ( p ) tends to peak at  p  ~ 0.185 in copper oxide superconductors. This particular value of the hole content, often termed as the critical hole concentration, has several features putative to a quantum critical point (QCP). Very recently, the pressure dependences of the superconducting transition temperature ( T  c ) and the critical current ( I  c ) in pure CeRhIn 5  and Sn doped CeRhIn 5  heavy fermion compounds have been reported (Nature Communications (2018) 9:44, 10.1038/s41467-018-02899-5). The critical pressure demarcates an antiferromagnetic quantum critical point where both  T  c  and  I  c  are maximized. We have compared and contrasted this behavior with those found for Y 1− x  Ca  x  Ba 2 Cu 3 O 7− δ   in this brief communication. The resemblance of the systematic behavior of the critical current with pressure and hole content between heavy fermion systems and hole doped cuprates is significant. This adds to the circumstantial evidence that quantum critical physics probably plays a notable role behind the unconventional normal and superconducting state properties of copper oxide superconductors.

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Possible quantum critical behavior revealed by the critical current density of hole doped high-Tc cuprates in comparison to heavy fermion superconductors